Combine all ingredients in large heavy-bottomed pot; add 3 gallons water; bring to a boil; reduce heat; simmer 3 hours, skimming off impurities as they form on the surface; strain; chill; reserve in refrigerator.

Add cockles and a little cooking liquid from beans if needed, so liquid covers cockles; cover pot with a lid; steam until cockles open (about 4 minutes); remove from heat; discard any cockles that do not smell sweet.

To serve, discard thyme sprigs; spoon cockles, artichokes, and beans into large serving bowls; drizzle with oil; sprinkle with parsley.

Chef’s Note: Beans can also be cooked in large heavy-bottomed pot, covered, until tender (about 1 1/2 hours).